Vandermonde matrix
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an ( m + 1 ) × ( n + 1 ) {\displaystyle (m+1)\times (n+1)} matrix V = V ( x 0 , x 1 , ⋯ , x m ) = ( 1 x 0 x 0 2 … x 0 n 1 x 1 x 1 2 … x 1 n 1 x 2 x 2 2 … x 2 n ⋮ ⋮ ⋮ ⋱ ⋮ 1 x m x m 2 … x m n ) {\displaystyle V=V(x_{0},x_{1},\cdots ,x_{m})={\begin{pmatrix}1&x_{0}&x_{0}^{2}&\dots &x_{0}^{n}\\1&x_{1}&x_{1}^{2}&\dots &x_{1}^{n}\\1&x_{2}&x_{2}^{2}&\dots &x_{2}^{n}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&x_{m}&x_{m}^{2}&\dots &x_{m}^{n}\end{pmatrix}}} with entries V i , j = x i j {\displaystyle V_{i,j}=x_{i}^{j}} , the jth power of the number x i {\displaystyle x_{i}} , for all zero-based indices i {\displaystyle i} and j {\displaystyle j} . Some authors define the Vandermonde matrix as the transpose of the above matrix.